Asymptotically Isometric Copy of $l^{\beta}~(0<\beta<1)$ in Spaces of Bounded Linear Operators

DOI：10.3770/j.issn:1000-341X.2011.03.023

 作者 单位 智琛 天津理工大学理学院, 天津 300384 宋眉眉 天津理工大学理学院, 天津 300384

设$X$是赋范空间,任意$x^{\ast}\in S(X^{\ast})$都有达范点, $Y$是赋$\beta$范空间.如果存在$Y$的一个商空间渐近等距于$l^{\beta}$,那么算子空间$L(X,Y)$包含$l^{\beta}$的渐近等距翻版.并且,本文给出了$L(X,Y)$中有界闭的$\beta$-凸子集没有不动点性质的充分条件.

Assume $X$ is a normed space, every $x^{\ast}\in S(X^{\ast})$ can reach its norm at some point in $B(X)$, and $Y$ is a $\beta$-normed space. If there is a quotient space of $Y$ which is asymptotically isometric to $l^{\beta}$, then $L(X,Y)$ contains an asymptotically isometric copy of $l^{\beta}$. Some sufficient conditions are given under which $L(X,Y)$ fails to have the fixed point property for nonexpansive mappings on closed bounded $\beta$-convex subsets of $L(X,Y)$.